Limitations of quantum coset states for graph isomorphism
نویسندگان
چکیده
منابع مشابه
Limitations of single coset states and quantum algorithms for code equivalence
Quantum computers can break the RSA, El Gamal, and elliptic curve public-key cryptosystems, as they can efficiently factor integers and extract discrete logarithms. The power of such quantum attacks lies in quantum Fourier sampling, an algorithmic paradigm based on generating and measuring coset states. In this article we extend previous negative results of quantum Fourier sampling for Graph Is...
متن کاملLimitations of Algebraic Approaches to Graph Isomorphism Testing
We investigate the power of graph isomorphism algorithms based on algebraic reasoning techniques like Gröbner basis computation. The idea of these algorithms is to encode two graphs into a system of equations that are satisfiable if and only if if the graphs are isomorphic, and then to (try to) decide satisfiability of the system using, for example, the Gröbner basis algorithm. In some cases th...
متن کاملGraph isomorphism and adiabatic quantum computing
In the Graph Isomorphism (GI) problem two N -vertex graphs G and G′ are given and the task is to determine whether there exists a permutation of the vertices of G that preserves adjacency and transforms G → G′. If yes, then G and G′ are said to be isomorphic; otherwise they are non-isomorphic. The GI problem is an important problem in computer science and is thought to be of comparable difficul...
متن کاملA Quantum Observable for the Graph Isomorphism Problem
Suppose we are given two graphs on n vertices. We define an observable in the Hilbert space C[(Sn ≀ S2)m] which returns the answer “yes” with certainty if the graphs are isomorphic and “no” with probability at least 1 − n! 2 if the graphs are not isomorphic. We do not know if this observable is efficiently implementable.
متن کاملUniversality in Quantum Hall Systems: Coset Construction of Incompressible States
Incompressible Quantum Hall fluids (QHF’s) can be described in the scaling limit by three-dimensional topological field theories. Thanks to the correspondence between threedimensional topological field theories and two dimensional chiral conformal field theories (CCFT’s), we propose to study QHF’s from the point of view of CCFT’s. We derive consistency conditions and stability criteria for thos...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the ACM
سال: 2010
ISSN: 0004-5411,1557-735X
DOI: 10.1145/1857914.1857918